{
  "id": "2202.02134",
  "version": "v1",
  "published": "2022-02-04T13:53:19.000Z",
  "updated": "2022-02-04T13:53:19.000Z",
  "title": "On characteristic ideal of Selmer group associated to Artin representations",
  "authors": [
    "Dipramit Majumdar",
    "Subhasis Panda"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Selmer group for an Artin representation over totally real fields was studied by Greenberg and Vatsal. In this paper we study the Selmer groups for an Artin representation over a totally complex field. We establish an algebraic function of the characteristic ideal of the Selmer group associated to Artin representation over the cyclotomic $\\Z_p$- extension of the rational numbers under certain mild hypotheses and construct several examples to illustrate our result. We also prove that in this situation $\\mu$-invariant of the dual Selmer group is independent of the choice of the lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-04T13:53:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "artin representation",
      "characteristic ideal",
      "dual selmer group",
      "totally complex field",
      "totally real fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}